Systems and methods for determination of focus and telecentricity, amelioration of metrology induced effects and application to determination of precision bossung curves

ABSTRACT

An apparatus and method for the simultaneous determination of focus and source boresighting error for photolithographic steppers and scanners is described. A reticle containing custom arrays of box-in-box test structures specifically designed for performing source or exit pupil division using an aperture plate is exposed onto a resist coated wafer several times. The resulting exposure patterns are measured with a conventional overlay tool. The overlay data is processed with a slope-shift algorithm for the simultaneous determination of both focus and source telecentricity as a function of field position. Additionally, methods for ameliorating metrology induced effects and methods for producing precision Bossung curves are also described. This Abstract is provided for the sole purpose of complying with the Abstract requirement rules, it shall not be used to interpret or to limit the scope or the meaning of the claims.

CROSS REFERENCE TO RELATED APPLICATION:

This application claims the benefit of U.S. Provisional application Ser.No. 60/774,707 Feb. 17, 2006. The contents of which are incorporated byreference in its entirety.

OTHER REFERENCES

The below listed sources are incorporated herein by reference in theirentirety.

# Title Authors Journal Pages Date  63 Distinguishing Dose from Defocusfor In- C. Ausschnitt SPIE Vol. 3677 140:147 1999 Line LithographyControl 147 Quantifying the Capability of a New In-situ B. Roberts, et2000 Interferometer al. 303 A Comprehensive Guide To Optical C. MackFinle--division of KLA- 137:151 Lithography Simulation Tencor 229International Technology Roadmap for ITRS, 2001 Edition  1:17 2001Semiconductors, 2001 Edition, Lithography 459 PSM Polarimetry:Monitoring Polarization G. McIntyre, SPIE Vol. 5754-7 80:91 2005 at 193nm High-NA and Immersion with et al. Phase Shifting Masks 5,828,455Apparatus, Method of Measurement and A. Smith, et. U.S. Pat. No.5,828,455 1992 Method of Data Analysis For Correction of Al. OpticalSystem 6,079,256 Overlay Alignment Measurement of N. Bareket U.S. Pat.No. 6,079,256 2000 Wafers 6,356,345 B1 In-Situ Source MetrologyInstrument and B. McArthur, U.S. Pat. No. 6,356,345 1999 Method of Useet. Al 2005/0240895 Method of Emulation of Lithographic A. Smith, et. alU.S. Publication No. 2004 Projection Tools 2005/024895 2005/0243309Apparatus and Process for Determination A. Smith, et. al U.S.Publication No. 2004 of Dynamic Lens Field Curvature 2005/02433097,126,668 Apparatus and Process for Determination A. Smith, et. al U.S.Pat. No. 7,126,668 2004 of Dynamic Scan Field Curvature

FIELD OF THE INVENTION

The present invention relates generally to the field of semiconductorUltra Large Scale Integration (ULSI) manufacturing and more specificallyto techniques for characterizing the performance of photolithographicmachines and processes.

BACKGROUND OF THE INVENTION Background and Related Art

Typically one uses the term focal plane deviation (FPD) to measure theextent of lens or system dependent focal error over the entirelithographic imaging field. Lithographic systems with low to moderateamounts of focal plane deviation typically image better than those withgross amounts of focal plane deviation. Typically, the focal planedeviation associated with a photolithographic stepper or scanner ismeasured with some type of special lithographic imaging technique usingspecial reticle or mask patterns (See “Distinguishing Dose from Defocusfor In-Line Lithography Control”, C. Ausschnitt, SPIE Vo. 3677, pp.140-147, 1999; “Quantifying the Capability of a New In-situInterferometer”, B. Roberts et al, San Diego 2000 and U.S. Pat. No.6,356,345, for example). For fabs, Bossung plots (focus vs. CD) aretypically used as process aids to find the best focus as a function ofexposure dose and CD (critical dimension). These Bossung plots containplenty of inherent error (unknown focus budget effects) yet are stilluseful. While some focusing error or FPD stems from lens aberrations,other sources of focusing error include: stage non-flatness, stage tilt,wafer tilt, wafer surface irregularities, and scanner synchronizationerror (z). Traditional methods such as those mentioned above can usuallydetermine FPD but fail to separate-out the effects of other sourcesincluding scanner noise and wafer non-flatness. In addition, mosttraditional methods are not capable of separating-out systematic errorfrom random error—which is really needed for process controlapplications. As the semiconductor industry pushes the limits of opticallithography, focus or the effective z-height variation of the waferplane surface from that ideal position which provides the highestcontrast or otherwise optimal images is becoming difficult to controland measure. Extremely tight focus tolerance has lead to novel methodsto help improve the lithographic depth of focus as well as providingimproved methods for determining focus and focal plane deviation. Afirst example is given by Ausschnitt supra where a special reticlepattern containing features sensitive to exposure and focus shifts isused to separate-out dose effects from focus for lithographic processes.Another example can be found in U.S. Pat. No. 5,303,002 wherelongitudinal lo chromatic aberrations can be used to improve the overalllithographic depth of focus and improve focus latitude. A moreinteresting example can be found in Smith (see U.S. Publication No.2005/0243309 and U.S. Pat. No. 7,126,668) where a special reticlecontaining overlay targets is used to determine dynamic lens fieldcurvature to high accuracy in the presence of wafer non-flatness andscanner noise. A final example and used as part of U.S. Publication No.2005/0243309 and U.S. Pat. No. 7,126,668, can be found in U.S. Pat. No.5,828,455 where an in-situ interferometer is used to determine Zernikecoefficients using box-in-box structures for the proper characterizationof lens aberrations including focus.

While we have stressed the importance of determining focus, maintainingfocus control, and possibly improving the useable depth of focus weshould also mention that most lithographic scanner systems suffer fromseveral types of telecentricity error including source boresightingerror and telecentricities associated with both the entrance and exitpupil. For source telecentricity, error in the source centroid (energycentroid) in the presence of focusing error leads to problematic overlayerror and magnification error since misaligned sources produce rays thatimage reticle features at a net angular off-set through the resist.Overlay error, or the positional misalignment between patterned layersis an important concern as both the pitch and size of lithographicfeatures shrink since misaligned patterns are more likely to produceopen circuit conditions or poor device performance (Reference U.S. Pat.No. 6,079,256). Finally, since both overlay and focus controlspecifications will soon reach a few nanometers (Reference InternationalTechnology Roadmap for Semiconductors, 2001 Edition—Lithography”, ITRS,2001 Edition, pp. 1-17) methods that can accurately measure andseparate-out components related to focus and source telecentricity willbe highly desirable and required.

SUMMARY OF THE INVENTION

Having stressed the need for accurate methods of extracting focus andtelecentricity we now give a brief description of the preferredembodiment (FIG. 17 shows the exposure sequence for the two embodimentsof the present invention) where we simultaneously extract both focus(z-height with field position or FPD) and source boresighting error. Areticle containing an aperture plate with holes and arrays of box-in-boxtest structures (alignment attributes or overlay targets) is exposedonto a resist coated wafer several times—using positional stage shiftsbetween exposures (see FIGS. 1 and 11). The reticle with aperture plateis constructed in such a way as to perform source or exit pupil divisionduring the exposure (see theory section below). The resulting exposurepatterns are measured with a conventional overlay tool. The overlay datais processed with a slope-shift algorithm for the simultaneousdetermination of focus and source telecentricity, as a function of fieldposition. Knowledge of focus and source telecentricity as a function offield position allows for the correction of overlay error and improvedlithographic performance (improved contrast) when focus andtelecentricity metrics are entered into the machine subsystem controlhardware or appropriate optical lithography simulation softwarepackages. The methods of the preferred embodiment can be applied toproduction scanners during set-up and the results of the calculationscan be used to create accurate Bossung curves.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of the present invention taught herein areillustrated by way of example, and not by way of limitation, in the FIGsof the accompanying drawings, in which:

FIG. 1 shows the hardware layout cross-section for the first embodimentusing exit pupil division;

FIG. 2 a shows coordinates and notation relating to FIG. 1;

FIG. 2 b is a plan view and coordinates for FIG. 1;

FIG. 3 shows the effect of aperture plate below reticle in obstructingor occluding rays emanating from reticle plane RP;

FIG. 4 is a graphical illustration of effective source calculation fordetermining

$\frac{\mathbb{d}\overset{\_}{x}}{\mathbb{d}z};$

FIG. 5 shows the hardware layout cross-section for the first embodimentusing exit pupil division;

FIG. 6 shows the plan view of a single field point, exit pupil divisionZTEL, square aperture hole;

FIG. 7 shows the plan view of a single field point, exit pupil divisionarrangement, octagon;

FIG. 8 shows the reticle plan view layout for exit pupil division ZTEL,square aperture holes;

FIG. 9 shows unit cell cross section for exit pupil divisionarrangement, ZTEL;

FIG. 10 shows field point or reference array layout;

FIG. 11 shows the cross-section of ZTEL, source division arrangement;

FIG. 12 shows the effect of aperture plate on reticle back side onclipping the effective source;

FIG. 13 shows the reticle plan view for source division ZTEL with squareaperture holes;

FIG. 14 shows the cross-section of ZF cell;

FIG. 15 shows the plan view of ZF cell on source division arrangement;

FIG. 16 shows the plan view of ZED, extra dose structures;

FIG. 17 shows the exposure sequence for ZTEL;

FIG. 18 shows completed alignment attributes after ZF, ZREF and possibleZED exposures;

FIG. 19 a shows illumination geometry for source division arrangementextraction of telecentricity;

FIG. 19 b shows 1-d intensity profiles in direction cosine spacecorresponding to FIG. 19 a;

FIG. 20 shows the relation of source and entrance/exit pupiltelecentricities;

FIG. 21 shows combined large and small featured alignment attributes asZF structure in exit pupil division arrangement; only left (AAL) andcenter alignment attributes are shown;

FIG. 22 is an illustration of combination of source size (NAs) andfeature diffractive blur (ΔnD);

FIG. 23 shows the geometry and rotation for shift calculation in thepresence of photoresist;

FIG. 24 shows simulation conditions and correlations;

FIG. 25 shows typical output results for a single simulation;

FIG. 26 shows the fit of simulated shift dx_sim to resist thicknessT_(r);

FIG. 27 shows correlations of further simulation results with ageometric model;

FIG. 28 shows simulation conditions, shift correlation with resistthickness, and correlation of simulations with geometric shift;

FIG. 29 shows correlation of simulated and geometric calculation ofresist shift, multiple cases;

FIG. 30 shows simulation conditions and results of coma induced featureshift;

FIG. 31 shows some aberration dependant feature shifts as a function offocus, F;

FIG. 32 a shows resist line notation/geometry;

FIG. 32 b shows resist space notation/geometry;

FIG. 33 shows separate line and space patterns formed by light incidenton the wafer at substantially angle Q;

FIG. 34 shows example out bar pattern for cancellation metrology inducedshift in features being made at an angle;

FIG. 35 shows the completed bar-in-bar pattern where metrology effect onthe outer bar pair has been eliminated;

FIG. 36 shows the opposite polarity bar-in-bar patterns for cancellingout metrology shift;

FIG. 37 shows the unit field point layout for Lithographic Test Reticle(LTR);

FIG. 38 shows the schematic layout of CZB block in Lithographic TestReticle (LTR);

FIG. 39 shows sample bright field, 90 nm node test structures withinCZB; and

FIG. 40 is a flow diagram and decision tree for 18 preferredembodiments.

It will be recognized that some or all of the FIGs are schematicrepresentations for purposes of illustration and do not necessarilydepict the actual relative sizes or locations of the elements shown. TheFIGs are provided for the purpose of illustrating one or moreembodiments of the invention with the explicit understanding that theywill not be used to limit the scope or the meaning of the claims

DETAILED DESCRIPTION OF THE INVENTION

In the following paragraphs, the present invention will be described indetail by way of example with reference to the attached drawings. Whilethis invention is capable of embodiment in many different forms, thereis shown in the drawings and will herein be described in detail specificembodiments, with the understanding that the present disclosure is to beconsidered as an example of the principles of the invention and notintended to limit the invention to the specific embodiments shown anddescribed. That is, throughout this description, the embodiments andexamples shown should be considered as exemplars, rather than aslimitations on the present invention. Descriptions of well knowncomponents, methods and/or processing techniques are omitted so as tonot unnecessarily obscure the invention. As used herein, the “presentinvention” refers to any one of the embodiments of the inventiondescribed herein, and any equivalents. Furthermore, reference to variousfeature(s) of the “present invention” throughout this document does notmean that all claimed embodiments or methods must include the referencedfeature(s).

For the purposes of clarity the terms ZF cells and ZF structures usedherein refer to arrays of box-in-box test structures and aperture plate.The overall flow diagram for an exemplary embodiment is illustrated inFIGS. 17 and 40.

Exit Pupil (or Source) Division

-   Step 1: a reticle containing arrays of box-in-box test structures is    provided (FIGS. 8 and 13).-   Step 2: expose first large area array of ZF cells (FIG. 6 or 15) at    nominal exposure dose for large features.-   Step 3 shift wafer stage to align reference arrays (ZREF FIG. 10)    over ZF cells (FIG. 18).-   Step 4: if required, expose extra dose structures (ZED) around    clipped (AAR, AAL) structures.-   Step 5: measure the resulting exposure patterns with a conventional    overlay tool.-   Step 6: enter data into analysis engine and solve for focus and    source telecentricity.

This invention consists of the following exemplary 18 embodiments (seeFIG. 40 for the flow of the preferred embodiments):

Emb. # Method 1 determination of focus and source boresighting errorusing Exit Pupil Division 2 determination of focus and sourceboresighting error using Source Division 3 determination of focus andsource boresighting error in the presence of entrance pupiltelecentricity using grating patterns and Exit Pupil Division 4determination of focus and source boresighting error in the presence ofentrance pupil telecentricity using grating patterns and Source Division5 determination of focus, source boresighting, entrance pupiltelecentricity, and exit pupil telecentricity using Exit PupilDivision - with and without aperture plate 6 determination of focus,source boresighting, entrance pupil telecentricity, and exit pupiltelecentricity using Source Division - with and without aperture plate 7determination of focus and source boresighting error in the presence ofaberrations using Exit Pupil Division 8 determination of focus andsource boresighting error in the presence of aberrations using SourceDivision 9 elimination of metrology induced error using Exit PupilDivision 10 elimination of metrology induced error using Source Division11 intrinsic removal of metrology induced error using line-spaceattributes using Exit Pupil 12 intrinsic removal of metrology inducederror using line-space attributes using Source Division 13 intrinsicremoval of metrology induced error using bright and dark-fieldattributes using Exit Pupil Division 14 intrinsic removal of metrologyinduced error using bright and dark-field attributes using SourceDivision 15 accurate Bossung curves using Exit Pupil Division andApparatus 16 accurate Bossung curves using Source Division and Apparatus17 determination of focus and telecentricity components using ZMAP andExit Pupil Division 18 determination of focus and telecentricitycomponents using ZMAP and Source DivisionTheory and Detail:

1^(st) Embodiment Exit Pupil Division

FIG. 1 shows a cross section view of an exit pupil division arrangement(for extracting both focus and source telecentricity) that clips rays(1:3) emerging from reticle plane RP at aperture plate AP. Thus, ofmarginal rays 1 and 3, 3 is intercepted and occluded by AP while 1 willpass through the scanner objective lens and onto the wafer plane (notshown). Axial ray 2 is just passed by AP. FIGS. 2 a and 2 b showrespectively cross sectional and plan views with coordinate conventionsdescribing the exit pupil division arrangement of FIG. 1. The symbols inFIGS. 2 a and 2 b mean:

XR=transverse position of general point in reticle (shown belowdifferently)

XA=transverse position of edge point of occluding edge on aperture plate

Z=reticle to aperture plate distance (perpendicular to respectiveplanes)

n _(TEL)=transverse direction cosines of entrance pupil chief ray onreticle side

n _(R)=transverse direction cosines of general ray emanating from pointXR on reticle

nA=normal vector in aperture plane pointing into occluding area ofaperture plate AP.

With this, and denoting X=transverse position of ray intersection inaperture plane, we have:

$\begin{matrix}{\overset{\_}{X} = {{\overset{\_}{X}}_{R} + {Z\frac{{\overset{\_}{n}}_{R}}{\sqrt{1 - n_{R}^{2}}}}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$Clipping by the aperture plate will limit the rays that can enter theimaging system (stepper or scanner) according to:

$\begin{matrix}{{\overset{\_}{nA} \cdot \frac{\left( {\overset{\_}{XA} - \overset{\_}{XR}} \right)}{Z}} \geq \frac{{\overset{\_}{n}}_{R} \cdot {\overset{\_}{n}}_{A}}{\sqrt{1 - n_{R}^{2}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$For an image side telecentric system (steppers and scanners used in ULSIphotolithography) the exit pupil or image side direction cosine, nx,(non-immersion system) is:nx=M( n _(R) − n _(TEL))   Equation 3and the non-occlusion condition (Equation 2) becomes:

$\begin{matrix}{{\overset{\_}{nA} \cdot \frac{\left( {\overset{\_}{XA} - \overset{\_}{XR}} \right)}{Z}} \geq \frac{\overset{\_}{nA} \cdot \left( {\frac{{\overset{\_}{n}}_{X}}{M} + {\overset{\_}{n}}_{TEL}} \right)}{\sqrt{1 - \left( {\frac{{\overset{\_}{n}}_{X}}{M} + {\overset{\_}{n}}_{TEL}} \right)^{2}}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$For a point on the reticle located directly above the aperture plateedge ( XA= XR) and an aperture that covers the left half plane (nA=1,0), we get:n1_(x) ≧−M·n1_(TEL) (see FIG. 3) and M=system de-magnification  Equation 5

So the effect of the aperture plate is to clip approximately the lefthalf of the exit pupil (FIG. 3). The utility of this for the reticlepatterns used in this embodiment is that changes in z-height(ΔZ=delta-focus) produce a transverse shift ( ΔX) of a feature (and weare here thinking of the inner or outer portion of a bar-in-bar orbox-in-box pattern as well as other alignment attributes) of:

                                      Equation  6$\overset{\_}{\Delta X} = \mspace{596mu}{{{\Delta Z} \cdot \frac{\mathbb{d}\overset{\_}{X}}{\mathbb{d}Z}}\text{which~~we~~use~~to~~find~~both~~focus~~and~~source~~telecentricity.}}$which we use to find both focus and source telecentricity.

In a first approximation,

$\frac{\mathbb{d}\overset{\_}{X}}{\mathbb{d}Z}$is determined by the centroid of the source convolved with the maskfeature Fourier transform as modified and clipped by the exit pupil(Equation 4). In terms of the effective source (S( nx)) the instrumentalslope shift (d X/dZ) induced by aperture plate AP is:

$\begin{matrix}{\frac{\mathbb{d}\overset{\_}{X}}{\mathbb{d}Z} = \frac{\left( {{< {nx} >},{< {ny} >}} \right)}{\left\lbrack {< {nx} >^{2}{+ {< {ny} >^{2}{+ {< {nz}^{2} >}}}}} \right\rbrack^{1/2}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$where:

nx,ny,nz

=∫d0 n (nx,ny,nz)S( n   Equation 8and, FIG. 4, expressed as an equation for the effective source is:

and

$\begin{matrix}{{\overset{\_}{n}}_{F} = {\left( {1,0} \right)\mspace{14mu}{for}\mspace{14mu}{vertical}\mspace{14mu}{space}}} \\{= {\left( {0,1} \right)\mspace{14mu}{for}\mspace{14mu}{horizontal}\mspace{14mu}{space}}}\end{matrix}$

SW=isolated space width

λ=scanner operating wavelength.

The clipping factor C( n _(x)) is just the non-occlusion condition(Equation 4), i.e.:

$\begin{matrix}{{C\left( {\overset{\_}{n}}_{X} \right)} = \left\{ \begin{matrix}1 & {{if}\mspace{14mu}{inequality}\mspace{14mu}{of}\mspace{14mu}{Equation}\mspace{14mu} 4\mspace{14mu}{obtains}} \\0 & {otherwise}\end{matrix} \right.} & {{Equation}\mspace{14mu} 10}\end{matrix}$

To get a rough estimate of the instrumental slope shift,

$\frac{\mathbb{d}\overset{\_}{X}}{\mathbb{d}Z},$we let n_(TEL)=0 (typically small) and ignore convolution. This leadsto, for a conventional source of numerical aperture NAs on the waferside:

$\begin{matrix}\begin{matrix}{\frac{\mathbb{d}\overset{\_}{X}}{\mathbb{d}Z} \approx {\int_{{- \pi}/2}^{\pi/2}{{\mathbb{d}\theta}{\int_{0}^{NAs}{{{\mathbb{d}n} \cdot n}\mspace{14mu} n\mspace{11mu}\cos\;{\theta/{\int_{{- \pi}/2}^{\pi/2}{{\mathbb{d}\theta}{\int_{0}^{NAs}\ {{\mathbb{d}n} \cdot n}}}}}}}}}} \\{= {{2 \cdot \frac{1}{3}}{{NA}_{S}^{3}/\pi}\frac{{NA}_{S}^{2}}{2}}} \\{= {\frac{4}{3\pi}{NA}_{S}}}\end{matrix} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Table 1 (infra) shows the slope shift as computed from Equation 11 forseveral conventional sources:

TABLE 1 NAs .3 .6 .8$\frac{dX}{dZ}\left\lbrack {{nm}\text{/}{nm}} \right\rbrack$ .13 .25 .34

Equation 11 and the results in Table 1 are for large

$\left( {{SW}\mspace{11mu}\text{>>}\mspace{11mu}\frac{\lambda}{2\;{NA}_{X}}} \right)$features. Decreasing the feature size (SW) and/or using gratingarrangements (see U.S. Pat. No. 6,079,256) will increase the transversesize (in nx) of effective source S(nx) (Equation 9) and thereby increaseslope shift d X/dZ. In general and in the practice of this invention,the best values, e.g., values that should be used in a commerciallithography software package, need to be computed directly from asimulation of the situation that includes all known (error orperformance) factors. That is, (see U.S. Pat. No. 6,356,345 B1) sources,aberrations (see U.S. Pat. No. 5,828,455), exit and entrancetelecentricity, resist effects, etc. (vide infra).

FIG. 5 shows an x-cross section of the complete unit cell of a device(ZTEL) utilizing exit pupil division. Middle or unclipped bar pattern(also called alignment attribute or AA) is situated far enough from theedges of the opening in the aperture plate that extreme rays 1 and 2 arenot intercepted by it. Extreme ray direction at reticle is set byentrance pupil size and telecentricity and is:

$\begin{matrix}{n_{R} = {\frac{NA}{M} + n_{TEL}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

An important role for middle or unclipped alignment attribute AAC isthat when combined with clipped alignment attribute AAL and AAR, we canextract the source boresighting or telecentricity error nBS (seediscussion in source division arrangement below). For central alignmentattribute (AAC) of transverse size DAA we require for the minimumaperture hole size, DA

$\begin{matrix}{{DA} > {{DAA} + {2 \cdot Z \cdot \frac{nR}{\sqrt{1 - n_{R}^{2}}}}\left( {{with}\mspace{14mu} Z\mspace{14mu}{as}\mspace{14mu}{the}\mspace{14mu}{aperture}\mspace{14mu}{plate}\mspace{14mu}{distance}} \right)}} & {{Equation}\mspace{14mu} 13}\end{matrix}$Exemplary aperture hole sizes are shown in Table 2 below. M=4,n_(TEL)=0.03 (largest typical non-telecon), DAA=0.05mm (˜10 μm box with2 μm wide spaces)

TABLE 2 Table of Minimum Aperture Hole Sizes, DA, for Exit PupilDivision ZTEL. NA_(X) = .95 NA_(X) = 1.5 Z = 1 mm .605 0.936 Z = 2 1.161.82 Z = 5 2.83 4.48

FIG. 6 shows a plan view of single field point or unit cell exit pupildivision ZTEL with a square hole in the aperture plate for the preferredembodiment. In another embodiment, FIG. 7 shows a plan view of singlefield point, exit pupil division arrangement, octagon aperture hole.

In this case, clipped alignment attributes are arranged on all eightsides of octagonal opening OC. FIG. 8 shows a reticle plan view layoutfor an exit pupil division ZTEL with square aperture holes. The RA arereference arrays which are AAs (alignment attributes) that arecomplimentary to the field point AAs (e.g., inner bar AAs at fieldpoints→ outer bar structures for reference array AAs). The referencearrays, RA, must not be obscured in any way by the aperture plate, sothe minimum transverse distance of aperture plate AP from any referencearray structure is given by:

$\begin{matrix}{{{d\;\min} = {\frac{DAA}{2} + {\frac{Z \cdot {nR}}{\sqrt{1 - n_{R}^{2}}}{where}\mspace{14mu} Z{\mspace{11mu}\;}{is}\mspace{14mu}{the}\mspace{11mu}{aperture}\mspace{14mu}{offset}}}}\;} & {{Equation}\mspace{14mu} 14}\end{matrix}$and nR is the maximum reticle side direction cosine which is:

$\begin{matrix}{{nR} = {\frac{{NA}_{X}}{M} + n_{TEL}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$with NA_(x) being the maximum exit pupil numerical aperture, M thereduction magnification, and n_(TEL) the maximum entrance pupiltelecentricity angle.

FIG. 9 shows cross-section of a unit cell or field point of an exitpupil division ZTEL for the first preferred embodiment. It is sized foruse on scanners with maximum NA_(x)=0.95, n_(TEL)=0.03, M=4. FIG. 10shows detail of the field point and individual reference array layout.

Having derived the offsets for Exit Pupil Division for the firstpreferred embodiment we proceed to derive the transverse shifts forSource Division and then perform the calculations for extracting bothfocus and source telecentricity—possibly, in the presence of othertelecentricity and metrology errors.

2^(nd) Embodiment Source Division

FIG. 11 shows a cross-section of an apparatus (ZTEL) for use indetermining focus and telecentricity using Source Division as analternative to Exit Pupil Division (see above). Source truncation by asingle straight edge attached to top of reticle is calculatedanalogously to exit pupil clipping—the results of which produce featureshifts with focus shifts.

Where;

nR=general source ray on the reticle side

Tr=Reticle thickness

For aperture located at XA with normal nA (nA-subscript), the rays thatget past the aperture place and illuminate a point at XR on the reticlesatisfy (non-occlusion condition):

$\begin{matrix}{{{\overset{\_}{n}}_{A} \cdot \frac{\left( {{\overset{\_}{X}}_{A} - {\overset{\_}{X}}_{R}} \right)}{T_{R}}} > \frac{{- {\overset{\_}{n}}_{R}} \cdot {\overset{\_}{n}}_{A}}{\sqrt{n_{r}^{2} - n_{R}^{2}}}} & {{Equation}\mspace{14mu} 16}\end{matrix}$Expressing this in terms of a source ray on the wafer side n _(s)=M( n_(R)− n _(TEL)) we get:

$\begin{matrix}{{{\overset{\_}{n}}_{A} \cdot \frac{\left( {{\overset{\_}{X}}_{A} - {\overset{\_}{X}}_{R}} \right)}{T_{R}}} > \frac{{- {\overset{\_}{n}}_{A}} \cdot \left( {\frac{{\overset{\_}{n}}_{S}}{M} + {\overset{\_}{n}}_{TEL}} \right)}{\sqrt{n_{r}^{2} - \left( {\frac{{\overset{\_}{n}}_{S}}{M} + {\overset{\_}{n}}_{TEL}} \right)^{2}}}} & {{Equation}\mspace{14mu} 17}\end{matrix}$where n_(r) is the reticle refractive index.

For a point on the reticle directly above the aperture plate edge and anaperture covering the left half plane, the effect of the aperture plateis to approximately clip off the right half of the source (FIG. 12). Theeffect of the clipping is to produce a transverse shift sensitivityproportional to z-height or focus.

An approximate formula using geometric optics (i.e., large feature onreticle plane) for the instrumental slope shift, d X/dZ is given byEquations 7 and 8 but where the effective source, S ( n _(s)) is givenby:

and clipping factor C(n_(S)) is given by:

$\begin{matrix}{{C\left( n_{S} \right)} = \left\{ \begin{matrix}{1\mspace{14mu}{when}\mspace{14mu}{non}\text{-}{occlusion}\mspace{14mu}{condition}\mspace{14mu}\left( {{Equation}\mspace{14mu} 17} \right)\mspace{14mu}{is}\mspace{14mu}{satisfied}} \\{0\mspace{14mu}{otherwise}}\end{matrix} \right.} & {{Equation}\mspace{14mu} 19}\end{matrix}$A rough estimate of d X/dZ, same as for exit pupil clipping (Equation11) is:d X/dZ≈0.424 NA _(s)   Equation 20

The aperture plate opening size is determined by a similar considerationto exit pupil clipping case and leads to formula:

$\begin{matrix}{{DA} > {{2 \cdot T_{r} \cdot {\tan\left( {a\;{\sin\left( {\frac{1}{n_{r}}\left( {\frac{{NA}_{X}}{M} + n_{TEL}} \right)} \right)}} \right)}} + {DAA}}} & {{Equation}\mspace{14mu} 21\; a}\end{matrix}$Where n_(r)=index of the glass reticle Table 3 has exemplary DAs.

TABLE 3 Table of Minimum Aperture Hole Sizes for Source Division ZTEL.DA [mm] NA_(X) = .95 T_(r) = .15″ 1.47 T_(r) = .25″ 2.39 n_(r) = 1.51 (λ= 248 nm) n_(TEL) = 0.03 (worst anticipated n_(TEL)) M = 4 DAA = .1

FIG. 13 shows a reticle plan view for a Source Division ZTEL with squareaperture holes. It contains a multiplicity of focus/telecentricitydetermining unit cells ZF, each of which interacts with its own openingin aperture plate AP to produce an instrumental slope shift d X/dZ.Reference box structures, ZR consist of un-occluded (by AP) alignmentattributes complementary to those in each ZF. Extra dose structures ZEDare used to expose clipped alignment attributes so we can compensate fortheir reduced gain (infra) and thereby utilize this device in scannersrunning at production settings. FIGS. 14 and 15 show cross-sectional andplan views of ZF cells for an exemplary design that works out to anNA_(x)=0.95. Reference array ZR is as in FIG. 10 only now separationfrom central alignment attribute AAC is 1.25 mm instead of the 2.4 mmshown for exit pupil division arrangement. Each square is an 80 μmsquare annulus with 8 μm thick bars (spaces). Extra dose structures,ZED, are shown in plan view in FIG. 16. They consist of large (˜400 μm)open squares on the reticle that can be centered on the clipped AA ofFIG. 15 by shifting the wafer for a separate exposure at dose<E0(E0=minimal clearing dose for a large feature).

The gain G (<1) caused by the aperture plate on the clipped features canbe written as:

$\begin{matrix}\frac{G = {\int{\frac{d^{2}n_{r}}{\sqrt{1 - n_{W}^{2}}}\frac{\mathbb{d}E}{\mathbb{d}0}\left( {\overset{\_}{n}}_{W} \right)◯\;{H\left\lbrack \mspace{14mu}{\frac{{\overset{\_}{n}}_{r} \cdot {\overset{\_}{n}}_{e}}{\sqrt{n_{re}^{2}} - n_{r}^{2}} < {\left( {{\overset{\_}{X}}_{r} - {\overset{\_}{X}}_{e}} \right) \cdot {{\overset{\_}{n}}_{e}/T_{re}}}} \right\rbrack}}}}{\frac{\int{\mathbb{d}^{2}n_{r}}}{\sqrt{1 - n_{W}^{2}}}\frac{\mathbb{d}E}{\mathbb{d}0}\left( {\overset{\_}{n}}_{W} \right)} & {{Equation}\mspace{14mu} 21\; b}\end{matrix}$which after some manipulation can be re-expressed as:

                                     Equation  22$G = \frac{\ {\int{{\mathbb{d}v}{\int^{a\sqrt{\frac{n_{re}^{2} - v^{2}}{1 + a^{2}}}}\frac{{\mathbb{d}u}{\frac{\mathbb{d}E}{\mathbb{d}0}\left\lbrack {\left( {{u\;{\overset{\_}{n}}_{e}} + {v\;{\overset{\_}{n}}_{ep}} - {\overset{\_}{nx}}_{TEL}} \right)\frac{M}{n_{i}}} \right\rbrack}}{\sqrt{1 - {\left( \frac{M}{n_{i}} \right)^{2}\left( {{u\;{\overset{\_}{n}}_{e}} + {v\;{\overset{\_}{n}}_{ep}} - {\overset{\_}{nx}}_{TEL}} \right)^{2}}}}}}}}{\frac{\int{{\mathbb{d}{udv}}{\frac{\mathbb{d}E}{\mathbb{d}0}\left\lbrack {\frac{M}{n_{i}}\left( {{u\;{\overset{\_}{n}}_{e}} + {v\;{\overset{\_}{n}}_{ep}} - {\overset{\_}{nx}}_{TEL}} \right)} \right\rbrack}}}{\sqrt{1 - {\left( \frac{M}{n_{i}} \right)^{2}\left( {{u\;{\overset{\_}{n}}_{e}} + {v\;{\overset{\_}{n}}_{ep}} - {\overset{\_}{nx}}_{TEL}} \right)^{2}}}}}$where:

u,v=integration variables over the aperture

X _(r)=AA position on reticle

X _(e)=aperture plate edge position

n _(e)=aperture plate normal pointing into occluded region at X _(e)

n _(ep)=(−ney, nex)=unit vector perpendicular to n _(e)

n_(w)=direction cosine at the wafer

nx _(TEL)=entrance pupil telecentricity

M, n_(i)=scanner reduction magnification, wafer side immersion index

${\frac{\mathbb{d}E}{\mathbb{d}0}\left( {\overset{\_}{n}\; w} \right)} = \begin{matrix}{{illumination}\mspace{20mu}{source}\mspace{14mu}{as}\mspace{14mu}{projected}} \\{{through}\mspace{14mu}{scanner}\mspace{14mu}{onto}\mspace{14mu}{wafer}\mspace{14mu}{side}}\end{matrix}$

T_(re)=T_(r)/n_(r)=reticle thickness/reticle refractive index anda=( X _(r) − X _(e))· n _(e) /T _(re)   Equation 23

Numerical evaluation of Equation 22 produces values in the rangeG=0.4-0.6 so that with a typical product level dose:E=n·E0 (E0 is clearing dose)   Equation 24Where n˜2:4 range the dose at the wafer for clipped alignment attributesis:

$\begin{matrix}{\frac{ECAA}{E\;\Phi} = {{G \cdot {\left. n \right.\sim 0.8}} - {2.4\mspace{14mu}{where}\mspace{14mu}{ECAA}\mspace{14mu}{is}\mspace{14mu}{energy}\mspace{14mu}{for}\mspace{14mu}{clearing}\mspace{14mu}{AA}}}} & {{Equation}\mspace{20mu} 25}\end{matrix}$and is therefore not always (ECAA/E0<1) capable of properly exposingclipped AAs. The purpose of ZED is to blanket expose a large (˜100 μm atwafer) region around each clipped AA so that total dose/E0 is≧1. FromEquation 25 we see that setting the ZED exposure dose EZED to:EZED/E0˜0.5   Equation 26will not wash out bar structures of clipped ZF and will allow underexposed bars to develop out. FIG. 17 illustrates the exposure sequence(process flow) for the ZTEL. It applies to both source and exit pupildivision embodiments.

Calculation Boresighting Error and Focus for the 1^(st) and 2^(nd)Embodiments:

FIG. 18 shows three completed alignment attributes (AAL′, AAC′, AAR′)after ZF, ZREF and possibly ZED exposures. To illustrate extraction ofboresighting error we first discuss the case of zero entrance(n_(TEL)=0) and exit pupil telecentricity. When alignment attributesAAL, AAC, AAR are large spaces or lines

$\left( {{SW}\operatorname{>>}\frac{\lambda}{2{NA}_{X}}} \right).$For a 1-d source with:

nBS=reticle side boresighting error>0

NA_(s)=source NA on reticle side

The directional centroid, <nx>is given approximately by:

nx

=∫dnx nx I(nx)/∫dnx I(nx)   Equation 27with the value of <nx> for AAL, AAC, AAR shown in FIG. 19 b. Now,

$\begin{matrix}\begin{matrix}{{\frac{\mathbb{d}x}{\mathbb{d}Z} \sim \left\langle {nxI} \right\rangle} = {{effective}\mspace{14mu}{source}\mspace{14mu}{centroid}\mspace{14mu}{at}\mspace{14mu}{wafer}}} \\{{in}\mspace{14mu}{immersion}\mspace{14mu}{medium}} \\{{= {{M \cdot} < {nx} > {/{nI}}}},{nI}} \\{= {{immersion}\mspace{14mu}{medium}\mspace{14mu}{index}}}\end{matrix} & {{Equation}\mspace{20mu} 28}\end{matrix}$AAL, AAC, AAR features are printed as inner boxes at focus position F1while the outer boxes are printed without the source shade present andat a possibly different focus, F2, and shifted (possibly) by T_(x).T_(x) shift is due to stage positioning errors. Using Equation 28 andthe results in FIG. 19 b, the x-shifts are calculated in Table 4 below:

TABLE 4 X-shifts Site Inner Box Outer Box L$\frac{M}{2\mspace{14mu}{nI}}\left( {{nBS} - {NA}_{S}} \right)F\; 1$${{\frac{M}{nI} \cdot {nBS} \cdot F}\; 2} + T_{X}$ C$\frac{M}{nI}{{nBS} \cdot F}\; 1$${{\frac{M}{nI} \cdot {nBS} \cdot F}\; 2} + T_{X}$ R$\frac{M}{2\mspace{14mu}{nI}}{\left( {{nBS} + {NA}_{S}} \right) \cdot F}\; 1$${{\frac{M}{nI} \cdot {nBS} \cdot F}\; 2} + T_{X}$The total measured bar-in-bar shift (BB) is just:BB=outer box position−inner box position   Equation 29We can extract F1 by looking at:

$\begin{matrix}{{{BBL} - {BBR}} = {{\frac{M \cdot {NA}_{S}}{nI} \cdot F}\; 1}} & {{Equation}\mspace{20mu} 30}\end{matrix}$since M, nI, NA_(S) are otherwise known, we get the focus value F1:

$\begin{matrix}{{F\; 1} = {\frac{nI}{M \cdot {NA}_{S}}\left( {{BBL} - {BBR}} \right)}} & {{Equation}\mspace{20mu} 31}\end{matrix}$We can extract nBS, the source boresighting or telecentricity error, bylooking at:

$\begin{matrix}{{{BBR} + {BBL} - {2{BBC}}} = {{- \frac{M \cdot {nBS}}{nI}}F\; 1}} & {{Equation}\mspace{20mu} 32} \\{{so}\mspace{14mu}{that}\text{:}} & \; \\{{nBS} = {\frac{nI}{{M \cdot F}\; 1}\left\lbrack {{2 \cdot {BBC}} - {BBR} - {BBL}} \right\rbrack}} & {{Equation}\mspace{20mu} 33}\end{matrix}$

For this embodiment, we are especially sensitive to nBS when running outof focus (i.e., F1˜1 μm). So, if we are particularly interested in nBS,because these exposures are carried out with large features, we can runsignificantly (F1/1 μm) out of focus to increase our sensitivity to nBS.

The above discussion applies to both source and exit pupil divisionarrangements. FIG. 20 illustrates the relation of entrance pupil/exitpupil and source centroids. In the presence of wafer reticle sidetelecentricity (nxi, n_(TEL)≠0) the x-shifts of Table 4 become:

TABLE 5 X-shifts for Large Features. Site ΔX (inner box) ΔX (outer box)L$F\;{1\left\lbrack {{nxi} + {\frac{M}{2\mspace{11mu}{nI}}\left( {{nBS} - n_{TEL} - {NA}_{S}} \right)}} \right\rbrack}$${F\;{2\left\lbrack {{nxi} + {\frac{M}{nI}n_{TEL}}} \right\rbrack}} + T_{X}$C$F\;{1\left\lbrack {{nxi} + {\frac{M}{nI}\left( {n_{TEL} + {nBS}} \right)}} \right\rbrack}$${F\;{2\left\lbrack {{nxi} + {\frac{M}{nI}n_{TEL}}} \right\rbrack}} + T_{X}$R$F\;{1\left\lbrack {{nxi} + {\frac{M}{2\mspace{14mu}{nI}}\left( {{nBS} - n_{TEL} + {NA}_{S}} \right)}} \right\rbrack}$${F\;{2\left\lbrack {{nxi} + {\frac{M}{nI}n_{TEL}}} \right\rbrack}} + T_{X}$As before, we can get F1:

$\begin{matrix}{{F\; 1} = {\frac{nI}{M \cdot {NA}_{S}}\left( {{BBL} - {BBR}} \right)}} & {{Equation}\mspace{20mu} 34}\end{matrix}$while only the combination nBS+3·n_(TEL) we can extract from

$\begin{matrix}{{{nBS} + {3 \cdot n_{TEL}}} = {\frac{- {nI}}{F\;{1 \cdot M}}\left( {{BBR} + {BBL} - {2\;{BBC}}} \right)}} & {{Equation}\mspace{20mu} 35}\end{matrix}$

3^(rd) and 4^(th) Embodiments Source or Exit Pupil Division UsingAdditional Grating Patterns

If we utilize an exit pupil division arrangement with alignmentattributes AAL, AAC, AAR comprising diffractive gratings

$\left( {{\left. \frac{\lambda}{GP} \right.\sim{NA}_{e}} = {{entrance}\mspace{14mu}{pupil}\mspace{14mu}{numerical}\mspace{14mu}{aperture}}} \right)$such as those in U.S. Pat. No. 6,079,256 or small

$\left( {\left. {SW} \right.\sim\frac{\lambda}{2\;{NA}_{e}}} \right)$features then diffraction by our alignment attributes will fill up theentrance pupil and effectively wash out or minimize the effects ofsource structure (boresighting error and size). Reference marks, ZR, arealso exposed using small features so that we get for shifts the resultsof Table 6:

TABLE 6 X-shifts for ‘Small’ ZF Structures (Exit Pupil Division) and‘Large’ ZR Structures. Site ΔX (inner box) ΔX (outer box) L$F\;{1\left\lbrack {{nxi} + {\frac{M}{nI} \cdot \frac{{NA}_{e}}{2}}} \right\rbrack}$F2 · nxi + T_(X) C F1 · nxi F2 · nxi + T_(X) R$F\;{1\left\lbrack {{nxi} - {\frac{M}{nI} \cdot \frac{{NA}_{e}}{2}}} \right\rbrack}$F2 · nxi + T_(X)

Now by simultaneously combining small and large features into ZFstructures (FIG. 21) we can simultaneously print them at a single focus(F1) value. Reference structures ZR will be the alignment attributescomplementary to AAL and AAC shown in FIG. 21 but will be completelyunoccluded by aperture plate AP. From inspection of Tables 5 and 6, weeasily see that:

$\begin{matrix}{\mspace{20mu}{{{BBC}_{large} - {BBC}_{small}} = {F\;{1 \cdot \frac{M}{n\; I}}\left( {n_{TEL} + n_{BS}} \right)}}} & {{Equation}\mspace{14mu} 36} \\{{{BBR}_{large} + {BBL}_{large} - {2\;{BBC}_{small}}} = {\frac{F\;{1 \cdot M}}{n\; I}\left( {n_{BS} - n_{TEL}} \right)}} & {{Equation}\mspace{14mu} 37}\end{matrix}$where:

BBC_(small/large)=BB measurement from small/large featured centralalignment attribute (AAC)

BBR/BBL_(large)=BB measurement from right/left large featured alignmentattribute (AAR/AAL). Since F1 is known from Equation 31 or 34, weindependently get nBS and n_(TEL.)

Fifth and Sixth Embodiments Extracting Exit Pupil Telecentricity UsingSource or Exit Division

Further measurements will allow us to get exit pupil telecentricity nxi.For example, if we expose the ZF structures at a relatively large F1˜+1μm and use as a reference a separate reticle with an array of ZRstructures (no aperture plate present on second reticle) spatiallyco-incident with each ZF structure, and exposed at a second purposefullyshifted focus position F2˜−1 μm, then by looking at BBC_(small) orBBC_(large), we will be able to extract nxi over the projected field ofZFs to within a few transverse spatial modes dependent only on theexposure mode used. Thus for determining nxi over a static field(stepper or scanner) it will be determined as a function of fieldposition (x,y) to within a net translation and rotation viz:nxi (x,y)= nxi (x,y)|_(known)+(a−b·x, c+b·Y)   Equation 38where a, b, c are unknown constants.Detailed Consideration of Feature Shifts

Hitherto we have used relatively simple models for calculatinginstrumental slope shifts (dx/dZ). To the extent that we are imaginglarge features at the reticle, the feature will shift spatially as afunction of z-height (focus), linearly along the direction of the sourcetelecentricity. By large feature, we mean a feature that has arelatively small diffractive radius, Δn_(D) so that the angular size ofthe source and the diffractive spreading fits within the exit pupil(FIG. 22), the following relation obtains:NA_(S)+2Δn_(D)□NA   Equation 39Now even in the relatively simple situation we have neglected the finitephotoresist thickness (T_(r)) and refractive index (n_(r)) that willdiffer from our immersion media (FIG. 23). In FIG. 23:

-   -   F=focal value of incident light    -   F<0→the focus or ray convergence occurs a distance |F| above the        resist (Z=F); transverse position where rays converge is X=0    -   F=0→rays converge at resist top (Z=0) at X=0    -   F>0→rays converge F below resist top at Z=F, X=0.        Then the image shift while propagating through the resist is        given by:

$\begin{matrix}\begin{matrix}{{{\overset{\_}{XC}(Z)} = {{transverse}\mspace{14mu}{centroid}\mspace{14mu}{of}\mspace{14mu}{ray}}}\mspace{14mu}} \\{{bundle}\mspace{14mu}{at}\mspace{14mu} Z\mspace{14mu}{from}\mspace{14mu}{resist}\mspace{14mu}{top}} \\{{{{= {Z\frac{\mathbb{d}\overset{\_}{x}}{\mathbb{d}Z}}}}_{r} - {F\frac{\mathbb{d}\overset{\_}{x}}{\mathbb{d}Z}}}}_{i}\end{matrix} & {{Equation}\mspace{14mu} 40}\end{matrix}$where we must separately calculate instrument slopes in resist

$\left. \left( \frac{\mathbb{d}x}{\mathbb{d}Z} \right._{r} \right)$and immersion media

$\left. \left( \frac{\mathbb{d}x}{\mathbb{d}Z} \right._{i} \right).$

Again, we can derive formulas utilizing simple geometric ideas. Thus fora reticle side source telecentricity ( ns_(TEL)) and telecentricentrance pupil ( n _(TEL)=0) for an un-occluded alignment attribute wewould have:

$\begin{matrix}{{\frac{\mathbb{d}\overset{\_}{x}}{\mathbb{d}Z}}_{i} = {\frac{M}{n_{i}}{{\overset{\_}{n\; s}}_{TEL}/\sqrt{1 - {\left( \frac{M}{n_{i}} \right)^{2}{\overset{\_}{n\; s}}_{TEL}^{2}}}}}} & {{Equation}\mspace{14mu} 41}\end{matrix}$The above formula is in the immersion medium (i). Once in thephotoresist, the shift changes to:

$\begin{matrix}{{\frac{\mathbb{d}\overset{\_}{x}}{\mathbb{d}Z}}_{r} = {\frac{M}{n_{r}}{{\overset{\_}{n\; s}}_{TEL}/\sqrt{1 - {\left( \frac{M}{n_{r}} \right)^{2}n\; s_{TEL}^{2}}}}}} & {{Equation}\mspace{14mu} 42}\end{matrix}$We can also derive the more general formulas in presence of generalnon-telecentricity and boresighting errors and compare them withsimulations (see above discussion for example).Comparison with Resist Simulations:

FIG. 24 shows a comparison of a set of simulations of feature shift atresist bottom with geometric calculation. Overall correlation is good,however, there are some relatively large (˜7.5 nm or ˜30%) differencesfor resist thickness in 700-800 nm thickness range. FIG. 25 showstypical simulation output for a single simulation. A fourth orderpolynomial in T_(r) (FIG. 26) is required for reasonable fit, not thelinear fit indicated by Equation 40. FIG. 27 shows correlations ofsimulations over a wider range of focus and dose values. There are up to10 nm deviations from the simple geometric model. FIG. 28 showsvariation of shift with resist thickness. Up to 16 nm deviations fromlinear model and a cubic polynomial is required to fit shift to resistthickness variation.

Further simulations with the same conditions as in FIG. 28 but with athreshold model in air show deviations from the geometric model up to 8nm. Still further simulations using a threshold resist model show>10 nmdeviations from geometric model are present. FIG. 29 correlates all ofthe geometric and simulated shift data. High general correlation is goodbut for point by point use in metrology, less deviation is required thanshown. One of the conclusions from simulations is we cannot rely on thesimple geometric model of Equations 40, 41 and 42 to account for featureshift. Instead we need to use fits to simulation results.

Seventh and Eighth Embodiments Source Boresighting and Focus in thePresence of Aberrations

All of the above utilized zero wavefront aberrations. In the presence ofnon-zero wavefront aberrations, there will generally be a non-linearresponse (in F) of the shift caused by focus. FIG. 30 shows simulationconditions and results of coma induced feature shift. In the regioncentered around F=200 nm the shift is relatively independent of dose(E/E0) and can be written as:

$\begin{matrix}{{\Delta\;{X_{coma}(F)}} = {a\;{8 \cdot \frac{\mathbb{d}x}{{\mathbb{d}a}\; 8}}(F)}} & {{Equation}\mspace{14mu} 43}\end{matrix}$where:a8=X-coma aberration (radians)and dx/da8 is approximately given by:

$\begin{matrix}{{{\left. \frac{\mathbb{d}x}{{\mathbb{d}a}\; 8} \right.\sim 0.000267} \cdot \left( {z - 256.9} \right)^{2}} + {85.5\mspace{14mu}{nm}\text{/}{rad}}} & {{Equation}\mspace{14mu} 44}\end{matrix}$

FIG. 31 shows the results of multiple sets of simulations of this type.The conclusion from these considerations is that we typically need toknow the aberrations (a_(i)) as preferably determined by some in-situmethod (see U.S. Pat. No. 5,828,455) and include a term of the form:

$\begin{matrix}{{\Delta\;{X_{abb}(F)}} = {\sum\limits_{i = 1}^{n}{a_{i}\frac{\mathbb{d}x}{\mathbb{d}a_{i}}(F)}}} & {{Equation}\mspace{14mu} 45}\end{matrix}$on the right hand side of our BB equations (Equations 30 and 32) whensolving for F. The above simulations were for large features. Smallfeatures will have their own, unique

$\frac{\mathbb{d}x}{\mathbb{d}a_{i}}(F)$functions which need to be separately simulated.

Illumination source

$\left( \frac{\mathbb{d}E}{\mathbb{d}0} \right)$deviation from ideal as determined for instance by U.S. Pat. Nos.6,356,345 B1 or 6,741,338 B2 will also modify

$\frac{\mathbb{d}x}{\mathbb{d}Z}$and need to be taken into account.

9^(th) and 10^(th) Embodiments Amelioration of Metrology Induced Error

Metrology Effects, Theory:

While aberration and source imperfections complicate our determinationof focus and telecentricity, there exist good in-situ methods formeasuring them and subsequent simulations allow us to remove theireffects. Simulations (supra) utilize the bottom position of a line orspace as designating the shift. In practice, because of the relativelylarge slopes introduced by the focusing fiducials (ZF), the resist willnot have perpendicular or nearly perpendicular sidewalls. For a resistline we have (FIG. 32 a):

Left edge:XL(Z)=XL(T _(r))−(T _(r) −Z)tan(QL−π/2)   Equation 2.100

Right edge:XR(Z)=XR(T _(r))−(T _(r) −Z)tan(QR−π/2)   Equation 2.101while for a space in resist we have (FIG. 32 b):

Left edge:XL(Z)=XL(T _(r))+(T _(r) −Z)·tan(QL−π/2)   Equation 2.102

Right edge:XR(Z)=XR(T _(r))−(T _(r) −Z)·tan(QR−π/2)   Equation 2.103The repeated position by an overlay tool will be a combination of Zweighted edge positions. The weighting factor will generally depend onwhether the resist is overhanging (left edge of FIG. 32 a) or notoverhanging (right edge of FIG. 32 a). Wall angle QL or QR (supra)determines whether slope is overhanging or normal according to:Q>p/2 overhangingQ=0 vertical   Equation 2.104Q<p/2 normalThe edge weighting function will be a slight function of Q.WE(Z,Q)=edge weighting function for resist at depth Z and wall slope Q  Equation 2.105normalized as:

$\begin{matrix}{{\int_{0}^{T_{r}}\ {\frac{\mathbb{d}z}{T_{r}}{{WE}\left( {Z,Q} \right)}}} = 1} & {{Equation}\mspace{14mu} 2.106}\end{matrix}$Thus, the left edge of the line in FIG. 32 a would have measured edgelocation:

$\begin{matrix}\begin{matrix}{{XL}_{M} = \left\langle {{XL}(Z)} \right\rangle} \\{= {\int_{0}^{T_{r}}\ {\frac{\mathbb{d}z}{T_{r}}{{WE}\left( {Z,{QL}} \right)}{{XL}(Z)}}}} \\{= {{{XL}\left( T_{r} \right)} - {{{fh}({QL})} \cdot T_{r} \cdot {\tan\left( {{QL} - {\pi/2}} \right)}}}}\end{matrix} & {{Equation}\mspace{14mu} 2.107}\end{matrix}$where we have used the normalization condition of Equation 2.106 andintroduced the fractional height, fh:

$\begin{matrix}{{{fh}(Q)} = {\int_{0}^{T_{r}}\ {\frac{\mathbb{d}z}{T_{r}}\left( {1 - \frac{z}{T_{r}}} \right){{WE}\left( {Z,Q} \right)}}}} & {{Equation}\mspace{14mu} 2.108}\end{matrix}$Applying this to the other edges above we get Table 2.100.

TABLE 2.100 Measured Edge Locations with Metrology Model. Feature EdgeMeasured Edge Location Line Left XL(T_(r)) − fh(QL) * T_(r) * tan(QL −p/2) Line Right XR(T_(r)) + fh(QR) * T_(r) * tan(QR − p/2) Space LeftXL(T_(r)) + fh(QL) * T_(r) * tan(QL − p/2) Space Right XR(T_(r)) −fh(QR) * T_(r) * tan(QR − p/2)Line or feature center positions are of greatest interest in transversedisplacement measurements.They will be average of left and right edge locations and are in Table2.101.

TABLE 2.101 Measured Center Locations with Metrology Model. FeatureMeasured Feature Center Location = XCM Line $\begin{matrix}{{\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack} -} \\{\frac{1}{2}{T_{r}\left\lbrack {{{{fh}({QL})} \cdot {\tan\left( {{QL} - {\pi/2}} \right)}} - {{{fh}({QR})} \cdot {\tan\left( {{QR} - {\pi/2}} \right)}}} \right\rbrack}}\end{matrix}\quad$ Space $\begin{matrix}{{\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack} +} \\{\frac{1}{2}{T_{r}\left\lbrack {{{{fh}({QL})} \cdot {\tan\left( {{QL} - {\pi/2}} \right)}} - {{{fh}({QR})} \cdot {\tan\left( {{QR} - {\pi/2}} \right)}}} \right\rbrack}}\end{matrix}\quad$Looking at FIGS. 32 a and 32 b for a large feature, each edge formsindependently of one another so we would expect that:QR^(space)=QL^(line)QL^(space)=QR^(line)   Equation 2.109Furthermore, we would expect the feature center location at the bottomof the resist to be the same or:

$\begin{matrix}{{\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack}^{space} = {\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack}^{line}} & {{Equation}\mspace{14mu} 2.110}\end{matrix}$

Both of these expectations are borne out by simulation (Table 8).

TABLE 8 Sample Simulation Results Bearing out Equation 2.109 SymmetryBetween Large Line and Large Space Source: Conventional, NAs = 0.4,nxtel(wafer) = 0.05 Exit Pupil: Unobscured, NA = 0.8 Wavelength: 193 nmDose: E/E0 = 2 Mask1: 1500 nm line, 2500 nm space Mask2: 1500 nm space,2500 nm line Resist: 0 diffusion, no absorption, nr = 1.75, gamma model(g = 6) Mask 1 (line) Mask 2 (space) QL 93.33 89.36 QR 89.34 93.33 XC =½(XL + XR) 12.8 12.76 CD 1479.89 1520.16 CD-CDnom −20.11 20.16 XL−727.15 −747.32 XR 752.74 772.84 QR(space) − QL(line) 0 QL(space) −QR(line) 0.02From 2.109 and 2.110, the measured feature location will be the same forboth line and space:

$\begin{matrix}\begin{matrix}{{XCM}^{line} = {{\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack}^{line} -}} \\{\frac{1}{2}{T_{r}\begin{bmatrix}{{{fh}{\left( {QL}^{L} \right) \cdot {\tan\left( {{QL}^{L} - \pi} \right)}}} -} \\{{{fh}\left( {QR}^{L} \right)} \cdot {\tan\left( {{QR}^{L} - \frac{\pi}{2}} \right)}}\end{bmatrix}}} \\{= {{\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack}^{space} -}} \\{\frac{1}{2}{T_{r}\begin{bmatrix}{{{{fh}\left( {QR}^{S} \right)} \cdot {\tan\left( {{QR}^{S} - \frac{\pi}{2}} \right)}} -} \\{{{fh}\left( {QL}^{S} \right)} \cdot {\tan\left( {{QL}^{S} - \frac{\pi}{2}} \right)}}\end{bmatrix}}} \\{= {{\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack}^{space} +}} \\{\frac{1}{2}{T_{r}\begin{bmatrix}{{{fh}{\left( {QL}^{S} \right) \cdot {\tan\left( {{QL}^{S} - \frac{\pi}{2}} \right)}}} -} \\{{{fh}\left( {QR}^{S} \right)} \cdot {\tan\left( {{QR}^{S} - \frac{\pi}{2}} \right)}}\end{bmatrix}}} \\{= {XCM}^{space}}\end{matrix} & {{Equation}\mspace{14mu} 2.111}\end{matrix}$

Line and space have the same bottom shift, measured shift, and metrologyweighting correction. So, once we have our metrology model asrepresented by fractional height factor fh(Q) we can compensate formetrology induced shifts using Equation 2.111. The line/space symmetry(Equation 2.109) is illustrated in FIG. 33. Light with centroid angle=Qcreates large line and a large space. The shift in addition to

$\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack$from Table 2.101 (metrology shift) for line (ΔXL) and space (ΔXS) is:

$\begin{matrix}{{\Delta\;{XL}} = {\frac{- T_{r}}{2}\begin{bmatrix}{{{fh}\left( {Q\; 2} \right)} \cdot {\tan\left( {{Q\; 2} - \frac{\pi}{2}} \right)}} \\{{- {{fh}\left( {Q\; 1} \right)}} \cdot {\tan\left( {{Q\; 1} - \frac{\pi}{2}} \right)}}\end{bmatrix}}} & {{Equation}\mspace{14mu} 2.111{.1}} \\{{\Delta\;{XS}} = {\frac{T_{r}}{2}\begin{bmatrix}{{{fh}\left( {Q\; 1} \right)} \cdot {\tan\left( {{Q\; 1} - \frac{\pi}{2}} \right)}} \\{{- {{fh}\left( {Q\; 2} \right)}} \cdot {\tan\left( {{Q\; 2} - \frac{\pi}{2}} \right)}}\end{bmatrix}}} & {{Equation}\mspace{14mu} 2.111{.2}}\end{matrix}$

Now, independent of the functional form of fh(Q) the metrology inducedshifts (ΔXL and ΔXS of Equations 2.111.1 and 2.111.2) are opposite ofone another:ΔXL=−ΔXS   Equation 2.111

So again, knowing our metrology model parameters (fh(Q1)) allows us toremove metrology induced shifts (Equations 2.111.1 and 2.111.2) from ourBB measurement results.

11^(th) and 12^(th) Embodiments Intrinsic Removal of the MetrologyEffect for Both Source and Exit Pupil Divisions:

Now, one arrangement that suggests itself and allows for elimination oreffective removal of the metrology induced shift consists of creatingline and space patterns simultaneously for the inner (or outer) set ofbars. If in, say, the left alignment attribute (AAL) in FIG. 21 we lookat the reticle in cross-section PP, its side view would be as in the topof FIG. 34. The left bar would consist of an isolated large space(prints at ˜1 μm at wafer) while the right bar would consist of anisolated large line (˜1 μm at wafer). When setting up the metrologygates, the right bar gates could be well inside the ˜5 μm cleared resistarea on each side of the right isolated line. Then,

$\begin{matrix}\begin{matrix}{{\Delta\; X} = {{shift}\mspace{14mu}{of}\mspace{14mu}{bar}\mspace{14mu}{pair}\mspace{14mu}{of}\mspace{14mu}{{FIG}.\mspace{11mu} 34}}} \\{= {\frac{1}{2}\begin{Bmatrix}{{\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack}^{space} + {\Delta\;{XL}} +} \\{{\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack}^{line} + {\Delta\;{XS}}}\end{Bmatrix}}} \\{= {\frac{1}{2}\begin{Bmatrix}{{\frac{1}{2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack}^{space} +} \\{\frac{1}{\; 2}\left\lbrack {{{XL}\left( T_{r} \right)} + {{XR}\left( T_{r} \right)}} \right\rbrack}^{line}\end{Bmatrix}}}\end{matrix} & {{Equation}\mspace{14mu} 2.112}\end{matrix}$because of Equation 2.111.

The importance of Equation 2.112 is it completely eliminates themetrology effect (fh(Q)) and our having to otherwise measure andcalibrate it out. This arrangement could be applied to ISI patterns(U.S. Pat. No. 5,828,455) to eliminate metrology effects.

13^(th) and 14^(th) Embodiments Intrinsic Removal Using Bright and DarkField Imaging

Another arrangement for canceling metrology shift utilizes pairs ofalignment attributes of opposite polarity i.e., line and space disposedalong the same edge of aperture plate AP (FIG. 36). This requiresmeasuring twice as many BB patterns and averaging the results but againeliminates the need for a metrology model.

Average of line and space pattern gives us intrinsic shift only:

$\begin{matrix}{{\frac{1}{2}\left( {{BBA} + {BBB}} \right)} = {{{BB} + \underset{0}{\underset{︸}{\frac{1}{2}\left( {{\Delta\;{XL}} + {\Delta\;{XS}}} \right)}}} = {BB}}} & {{Equation}\mspace{14mu} 2.114}\end{matrix}$

15^(th) and 16^(th) Embodiments Determination of Precision BossungCurves

Measurement of Precision Bossung Curves

Bossung curves or CD/shift versus focus at varying dose levels are thequantitative starting point for semiconductor process monitoring andcontrol (see background above). They can be emulated (see e.g. U.S.Publication No. 2005/0240895) but are typically directly measured usingCD-SEM and/or overlay tool. FIG. 30 shows a typical set of Bossungcurves, in this case simulated. Now, due to wafer surface heightvariation, focus drift and jitter, the nominal focus value, especiallyrelative to the top of the photoresist, is typically the least certainportion of experimental Bossung curve determination. Combining thesource or exit pupil division arrangements (see above embodiments) withproduct features or test structures can greatly increase the speed andaccuracy of Bossung curve determination. A unit cell arrangement usefulout to NA=0.95 in a source division layout is shown in FIG. 37. Itconsists of a ZF structure with four clipped alignment attributes (AAL,AAR, AAT, AAB) and one central unclipped alignment attribute, AAC. Thereis a central feature and block, CZB, potentially as large as 0.912×0.912mm² that contains AAC and any product or test structures. CZB is locatedfar enough away from occluding edges of aperture place AP that allstructures within CZB are unaffected by it. This means that like AAC,they will not have the source or entrance pupil blocked by AP and thesefeatures will print just as they would on a reticle not having apertureplate AP. The presence of aperture plate and AAL, AAR, AAT, AAB and AACstructures lets us precisely determine the exact state of focus andtelecentricity present when product/test features in CZB print.

So doing the usual CD measurements accompanied by F determinationpermits experimental evaluation of Bossung curves.

17^(th) and 18^(th) Embodiments Determining Focus Error Components andSource Boresighting Error using Source or Exit Division

So far we have discussed using the ZTEL (box-in-box) targets—usingSource or Exit Pupil Division to determine both focus and sourcetelecentricity—possibly in the presence of both entrance and exit pupiltelecentricity errors. The focus (z-height variation) so far describedin the preferred embodiment also known again as focal plane deviation orFPD (once known over the exposure field). As described in U.S.Publication No. 2005/0243309 and U.S. Pat. No. 7,126,668 one candetermine the focus error associated with the lens and other sourcessuch as wafer non-flatness and scanner noise using various types offocusing fiducials such as: PSM structures (Reference 459), SchnitzelTargets, FOCAL monitors, and ISI targets (see U.S. Pat. No. 5,828,455).These focusing monitors—mentioned in U.S. Publication No. 2005/0243309and U.S. Pat. No. 7,126,668—can be added to the reticle patternsdescribed in the above preferred embodiment and performed in parallelwith the present invention in order to extract the individual errorcomponents related to both FPD and telecentricity. FIG. 40 shows adecision tree flow diagram for each of the embodiments described above.

While the present invention has been described in conjunction withspecific preferred embodiments, it is evident that many alternatives,modifications and variations will be apparent to those skilled in theart in light of the foregoing description. It is therefore contemplatedthat the appended claims will embrace any such alternatives,modifications and variations as falling within the true scope and spiritof the present invention.

1. A method for determining focus and source telecentricity for alithographic projection machine comprising: providing a reticlecontaining arrays of box-in-box test structures and aperture plate forexit pupil division, said box-in-box test structures comprising at leastone set of large featured alignment attributes and one set of smallfeatured alignment attributes; exposing at least one array of thebox-in-box test structures; shifting wafer stage to align referencearrays over the box-in-box test structures; exposing the referencearrays; measuring the resulting exposure patterns with an overlay tool;and entering overlay data into an analysis engine, wherein the analysisengine is configured to solve for focus and source telecentricity. 2.The method of claim 1, wherein the lithographic projection machine isselected from a group consisting of a stepper and a scanner.
 3. Themethod of claim 1, wherein the exposure includes exposing extra dosestructures.
 4. The method of claim 1, wherein the overlay data iscorrected for aberrations.
 5. The method of claim 1, wherein the overlaydata is corrected for metrology error.
 6. The method of claim 1, whereinthe analysis engine is configured to solve for exit pupil telecentricityfrom the overlay data.
 7. The method of claim 1, wherein the analysisengine is configured to solve for entrance pupil telecentricity from theoverlay data.
 8. The method of claim 1, wherein the said reticle isconfigured for source division.
 9. The method of claim 1, wherein theanalysis engine includes lithography simulation.
 10. A method forproducing an optimized photolithographic chip mask work from alithographic projection machine and process, the method comprising:determining a focus result and a source telecentricity result whereinthe determining stem comprises: providing a reticle containing arrays ofbox-in-box test structures and aperture plate for exit pupil division,said box-in-box test structures comprising at least one set of largefeatured alignment attributes and one set of small featured alignmentattributes; exposing at least one array of the box-in-box teststructures; shifting wafer stage to align reference arrays over thebox-in-box test structures; exposing the reference arrays; measuring theresulting exposure patterns with an overlay tool; and entering overlaydata into an analysis engine, wherein the analysis engine is configuredto determine focus and source telecentricity; entering the focus and thesource telecentricity results into a machine simulator or controller;determining optimum operation conditions related to the machine andprocess to reflect the optimized conditions; and exposing productwafer(s) using the optimized conditions.
 11. A method for producing anoptimized photolithographic chip mask work from a lithographicprojection machine and process, the method comprising: determining focusand source telecentricity, wherein the determining step comprises:providing a reticle containing arrays of box-in-box test structures andaperture plate for exit pupil division, said box-in-box test structurescomprising at least one set of large featured alignment attributes andone set of small featured alignment attributes; exposing at least onearray of the box-in-box test structures; shifting wafer stage to alignreference arrays over the box-in-box test structures; exposing thereference arrays; measuring the resulting exposure patterns with anoverlay tool; and entering overlay data into an analysis engine, whereinthe analysis engine is configured to determining focus and sourcetelecentricity; entering the focus and source telecentricity resultsinto a machine simulator or controller; determining precision Bossungcurves related to the machine and process; and exposing product wafer(s)using the precision Bossung curves.